15.8.44 problem 46

Internal problem ID [3047]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 46
Date solved : Monday, January 27, 2025 at 07:11:38 AM
CAS classification : [[_homogeneous, `class G`], _rational, _Bernoulli]

\begin{align*} y+x y^{\prime }&=x^{3} y^{6} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.751 (sec). Leaf size: 53

dsolve([x*diff(y(x),x)+y(x)=x^3*y(x)^6,y(1) = 1],y(x), singsol=all)
 

\[ y = \frac {\left (-\sqrt {5}-1+i \sqrt {10-2 \sqrt {5}}\right ) 2^{{1}/{5}} \left (-x^{2} \left (3 x^{2}-5\right )^{4}\right )^{{1}/{5}}}{12 x^{3}-20 x} \]

✓ Solution by Mathematica

Time used: 1.062 (sec). Leaf size: 26

DSolve[{x*D[y[x],x]+y[x]==x^3*y[x]^6,{y[1]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\sqrt [5]{2}}{\sqrt [5]{5 x^3-3 x^5}} \]